Quandaries
and Queries 

Can you help me understand why the area of a equilateral triangle is the square root of 3 divided by 4 times the lenght of the side squared? student 

Hi, I drew a diagram of an equilateral triangle. Draw a line from the vertex to the midpoint of the base. Cut along this line and move half of the triangle to form a rectangle. If a is the length of a side of the equilateral triangle and h the height then this rectangle has area
The triangle below, which is half of the rectangle, is a right triangle, and hence, by Pythagoras' theorem
Thus h = sqrt( ^{3}/_{4} a^{2}) = ^{sqrt(3)}/_{2} a. Hence the area of the triangle is
Penny 

